Using Line Segment Tracking to enable ML-based Track Reconstruction in CMS

Technical Summary: Using Line Segment Tracking to Enable ML-based Track Reconstruction in CMS

Problem Statement
In the High-Luminosity LHC (HL-LHC) era, the CMS experiment will face average pileup conditions of $\langle\mu\rangle \approx 200$ simultaneous proton–proton interactions per bunch crossing. Under these high-occupancy conditions, charged-particle tracking becomes the most computationally expensive step in event reconstruction. Traditional Kalman filter-based algorithms are intrinsically sequential, causing their computational cost to grow steeply with hit density. This poses a significant challenge for meeting the latency budget of the Phase-2 High-Level Trigger (HLT), necessitating pattern recognition methods that are both computationally cheaper and naturally parallelizable. Furthermore, while machine learning (ML) has shown promise in event reconstruction, existing approaches often build tracks directly from raw detector hits. This forces models to learn complex physical effects (such as magnetic field bending and detector geometry) from scratch, without leveraging prior physics information.

Methodology
This work introduces a hybrid approach that utilizes Line Segment Tracking (LST) objects as input tokens for a deep learning model, rather than individual detector hits. The methodology proceeds as follows:

1. Tokenization via LST Triplets: The model uses LST triplets (T3) as input tokens. These objects are constructed from a bottom-up hierarchy in the Phase-2 Outer Tracker (OT):

   • Mini-doublets (MD): Link hits within a single $p_T$ module.
   • Line Segments (LS): Join two MDs in neighboring layers.
   • Triplets (T3): Merge two LSs sharing a middle MD.
     Unlike raw hits, T3s carry rich local structure, including position, direction, and a local transverse momentum ($p_T$) estimate derived from the correlated hit pairs. This provides the model with strong physics priors from the start.

2. Transformer Encoder with Geometric Sparse Attention:

   • Architecture: A Transformer encoder processes the unordered set of T3 tokens. The input features (49 per triplet, including coordinates, angles, and $p_T$) are projected to a 256-dimensional hidden space, passed through six self-attention blocks (8 heads each), and mapped to a 128-dimensional latent space.
   • Sparse Attention: To handle the quadratic scaling of standard attention with $\sim 10^4$ tokens per event, the model employs a geometrically masked sparse self-attention. A token $i$ attends only to neighbors $j$ where $\Delta R_{ij} \leq 0.1$ in $\eta-\phi$ space. This reduces computational complexity from $O(N^2)$ to $O(Nk)$, where $k$ is the number of nearest neighbors, while preserving physically relevant context.

3. Object Condensation and Clustering:

   • Objective: The network is trained using an object condensation loss function. This objective assigns each token a "condensation charge" ($\beta \in [0,1]$) representing its likelihood of being a representative point for an object. The loss includes attractive terms (pulling constituents of an object toward a condensation point), repulsive terms (separating different objects), and a term that suppresses charges for noise (fake triplets).
   • Inference: The learned embeddings are clustered using DBSCAN (Density-Based Spatial Clustering of Applications with Noise). This density-based algorithm requires no prior specification of the number of clusters, allowing it to adapt to the variable track multiplicity of each event. A threshold on the condensation likelihood ($\beta \geq 0.005$) is applied prior to clustering to filter out low-confidence fake triplets.

Key Contributions

• First CMS ML Track Reconstruction: This paper presents the first demonstration of a track-reconstruction model in CMS that utilizes LST objects as tokens, bridging the gap between traditional combinatorial algorithms and modern ML architectures.
• Physics-Informed Tokenization: By using LST triplets instead of raw hits, the model incorporates detector-level information (geometry, $p_T$ estimates) directly into the input representation, reducing the learning burden on the network.
• Scalable Architecture: The implementation of geometrically masked sparse attention enables the processing of high-multiplicity events ($\sim 10^4$ tokens) on modern GPUs, addressing the scalability issues of standard Transformers in high-pileup environments.
• Single-Step Inference: The pipeline assembles full tracks in a single inference step using object condensation and DBSCAN, avoiding the sequential nature of traditional track building.

Results
The approach was evaluated on simulated $t\bar{t}$ events at $\langle\mu\rangle = 200$ using the Phase-2 detector geometry, comparing the "Transformer OC" model against the standard LST quintuplet (T5) baseline:

• Fake Rate Reduction: The model achieves a fake rate roughly three times lower than the T5 baseline across most of the acceptance (e.g., dropping to $\sim 0.05$ at high $p_T$ compared to the baseline's $\sim 0.18$).
• Duplicate Suppression: The duplicate rate is consistent with zero across all kinematic regions. In contrast, the T5 baseline exhibits duplicate rates rising from 0.04 to 0.15, as the combinatorial nature of LST can produce overlapping quintuplets for a single particle.
• Efficiency:
  • Under a strict requirement of spanning at least 5 layers ($N_L \geq 5$), the model shows a modest efficiency deficit (approx. 10 percentage points lower) compared to the T5 baseline in the core acceptance.
  • However, when the requirement is relaxed to $N_L \geq 4$ to recover shorter trajectories, the model matches or exceeds the T5 baseline efficiency (reaching 0.80–0.87 vs. 0.70–0.80) across the full acceptance, particularly in the forward region ($1 \lesssim |\eta| \lesssim 2$).
• Fake Rejection: The condensation likelihood effectively separates real triplets from fakes, retaining ~80% of true triplets while accepting only ~2% of fakes (ROC AUC = 0.93).

Significance and Claims
The paper claims that this work demonstrates the promise of advanced ML architectures for next-generation particle tracking under the harsh conditions of the HL-LHC. By leveraging LST objects as a "physics-rich tokenization," the model successfully incorporates detector geometry and momentum constraints, allowing it to match or surpass state-of-the-art combinatorial algorithms in purity and duplicate suppression.

The author explicitly states that this is a standalone algorithmic demonstration and should be viewed independently of official CMS tracking benchmarks. The significance lies in proving that a physics-informed ML model can handle high-pileup environments effectively. The natural next steps identified by the author is to integrate this model into the CMS reconstruction and trigger software alongside LST, measure its throughput against the Phase-2 HLT latency budget, and extend the approach from the Outer Tracker to the full tracking volume.